..then what's up with your parents?

Were they crappy, unknowledgable "dragonborns" or what?

afaik being dragonborn is a gift from the gods, so ur parents didnt have to be dragonborn

although your kids would be, we wont be having any of those because in the next we've disappeared never to be seen again

Not by blood, but by Akatosh's blessing, you're born with the soul of a dragon.

Read "The Book of the Dragonborn".

Which is why at times throughout the game Alduin, Paarthurnax, and Odahviing all refer to you as 'Dovah' (Dragon), not just 'Dovahkiin'. To them, since Akatosh gave you the Soul of a Dragon, you are a Dragon (and they are correct), but trapped in a mortal's body.